Abstract
We define the twisted loop Lie algebra of a finite dimensional Lie algebra \(\mathfrak{g}\) as the Fréchet space of all twisted periodic smooth mappings from \(\mathbb{R}\) to \(\mathfrak{g}\). Here the Lie algebra operation is continuous. We call such Lie algebras Fréchet Lie algebras. We introduce the notion of an integrable \(\mathbb{Z}\)-gradation of a Fréchet Lie algebra, and find all inequivalent integrable \(\mathbb{Z}\)-gradations with finite dimensional grading subspaces of twisted loop Lie algebras of complex simple Lie algebras.
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Communicated by L. Takhtajan
On leave of absence from the Institute for Nuclear Research of the Russian Academy of Sciences, 117312 Moscow, Russia.
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Nirov, K.S., Razumov, A.V. On \(\mathbb{Z}\)-Gradations of Twisted Loop Lie Algebras of Complex Simple Lie Algebras. Commun. Math. Phys. 267, 587–610 (2006). https://doi.org/10.1007/s00220-006-0068-3
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DOI: https://doi.org/10.1007/s00220-006-0068-3